Torsion of cylindrically anisotropic nano/microtubes of the cubic crystals obtained by rolling the crystal planes (011)

R. Goldstein, V. Gorodtsov, D. Lisovenko show affiliations and emails
Received  08 October 2016; Accepted  18 October 2016
Citation: R. Goldstein, V. Gorodtsov, D. Lisovenko. Torsion of cylindrically anisotropic nano/microtubes of the cubic crystals obtained by rolling the crystal planes (011). Lett. Mater., 2016, 6(4) 249-252
BibTex   https://doi.org/10.22226/2410-3535-2016-4-249-252

Abstract

Elastic torsion of cylindrically anisotropic nano/microtubes is examined by Saint-Venant approach. It is assumed that the tubes were obtained by rolling the plates of the cubic crystals with plane orientation (011). The analytical expression for the torsional stiffness for such nano/microtubes is obtained. Torsional stiffness is dependent on three compliance coefficients of cubic crystal, thickness parameter, chirality angle and radius of the tube. Numerical analysis of the torsional stiffness of nano/microtubes is made. This analysis showed that for most crystals the dimensionless ratio of torsional stiffness to torsional stiffness at zero chiral angle of nano/microtubes slightly varies with thickness parameter of tubes. Materials for which there is a substantial change in the dimensionless ratio of torsional stiffnesses, are revealed. Torsion of chiral nano/microtubes from cubic materials in the absence of tensile forces is accompanied by a linear Poynting’s effect. Сomparative analysis of the dimensionless ratios of torsional stiffness to torsional stiffness at zero chirality angle for nano/microtubes obtained by rolling the crystal planes (001) and (011) is given. It is shown that the variability of torsional stiffness for nano/microtubes obtained by rolling the crystal planes (011), is much higher than for nano/microtubes produced by rolling the crystal planes (001). Comparative analysis of linear Poynting’s effect for nano/microtubes obtained by rolling the crystal planes (001) and (011) is also given.

References (16)

1. V. Ya. Prinz, V. A. Seleznev, A. K. Gutakovsky, A. V. Chenovskiy, V. V. Preobrazhenskii, M. A. Putato, T. A. Gavrilova Physica E 6 (1-4) 828 - 831 (2000).
2. S. V. Golod, V. Ya. Prinz, V. I. Mashanov, A. K. Gutakovsky Semicond. Sci. Technolog. 16 (3) 181 - 185 (2001).
3. O. G. Schmidt, K. Eberl Nature 410 (6825) 168 (2001).
4. O. G. Schmidt, N. Schmarje, C. Deneke, C. Muller, N.-Y. Jin-Phillipp Adv. Mater 13 (10), 756 - 759 (2001).
5. V. Ya. Prinz Microelectr. Eng. 69 (2-4) 466 - 475 (2003).
6. Y. Mei, G. Huang, A. A. Solovev, S. Sanchez, E. B. Urena, I. Monch, F. Ding, T. Reindl, K. Y. Fu, P. K. Chu, O. G. Schmidt Adv. Mater 20 (21) 4085 - 4090 (2008).
7. Y. Mei, A. A. Solovev, S. Sanchez, O. G. Schmidt Chem. Soc. Rev. 40 (5) 2109 - 2119 (2011).
8. A. V. Eletskii Phys.Usp. 50 (3) 225 - 261 (2007) [А. В. Елецкий УФН 177 (3) 233 - 274 (2007)].
9. S. Reich, C. Thomsen, J. Maultzsch Carbon nanotubes: basic concepts and physical properties. Weinheim: Wiley-VCH. (2004) 467 p.
10. R. V. Goldstein, V. A. Gorodtsov, D. S. Lisovenko Phys. Mesomech. 12 (1-2) 38 - 53 (2009).
11. R. V. Goldstein, V. A. Gorodtsov, D. S. Lisovenko Doklady Physics 58 (9) 400 - 404. (2013).
12. R. V. Goldstein, V. A. Gorodtsov, D. S. Lisovenko Phys. Mesomech. 17 (2) 97 - 115 (2014).
13. R. V. Goldstein, V. A. Gorodtsov, D. S. Lisovenko Phys. Mesomech. 19 (3) 229 - 238 (2016).
14. R. V. Goldstein, V. A. Gorodtsov, A. V. Chentsov, S. V. Starikov, V. V. Stegailov, G. E. Norman Letters on Materials 1 (4) 185 - 189 (2011).
15. Landolt-Börnstein. Group III: Crystal and Solid State Physics. 29a. Second and Higher Order Constants. Berlin. Springer (1992).
16. J. H. Poynting Proc. Roy. Soc. A 82 (557), 546 - 559 (1909).

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